We'll go through each of the steps in the hypotheses test:

If the wheel is 'fair' then the probability of red and black are both 18/38 and the probability of green is 2/38.

\(H_0\colon p_{red}=\dfrac{18}{38}, p_{black}=\dfrac{18}{38}, p_{green}=\dfrac{2}{38}\)
\(H_a\colon\) at least one \(p_i\) is not as specified in the null

We can use the null hypothesis to check the assumption that all expected counts are at least 5.

\(Expected\;count=n (p_i)\)

With n = 100 we meet the assumptions needed to use Chi-square.

Let's use Minitab to calculate this.

First, enter the summarized data into a Minitab Worksheet.

1. After entering the data, select Stat > Tables > Chi-Square Goodness of Fit Test (One Variable)
2. Double-click Count to enter it into the Observed Counts box
3. Double-click Color to enter it into the Category names (optional) box
4. For Test select Input constants
5. Select Proportions specified by historical counts (this is what we would expect if the null was true)
6. Enter 18/38 for Black, 2/38 for Green and 18/38 for Red
7. Click OK

This should result in the following output: